Question

prove the following and please don't scam​

Answer 1

(i)

cos∅ x tan∅

cos∅ x sin∅/cos∅ (as tan∅ = sin∅/cos∅)

sin∅

LHS= RHS

(ii)

sin∅ x cot∅

sin∅ x cos∅/sin∅ (as cot∅ = cos∅/sin∅)

cos∅

LHS= RHS

Answer 2

Question :-

Prove that :

$\sf{(i) \cos \theta \tan \theta = \sin \theta} \\ \\ \sf{ (ii)\sin \theta \cot \theta = \cos \theta }$

Solution :-

To Prove :

$\sf{(i) \cos \theta \tan \theta = \sin \theta}$

Proof :

Let,

• $\sin \theta = \sf{ RHS}$

We know,

$\sf:\longmapsto{ \tan \theta = \frac{ \sin \theta }{ \cos \theta } }$

Then,

$\sf:\longmapsto{ \cancel {\cos \theta } \: \frac{ \sin \theta }{ \cancel{ \cos \theta }} = \sin \theta } \\ \\ \sf:\longmapsto{ \sin \theta = \sin \theta } \: \: \: \: \: \: \: \: \: \:$

Hence Proved !

==============================================

To prove :

$\sf{(ii) \sin \theta \cot \theta = \cos \theta}$

Proof :

Let,

• $\sf{ \cos \theta = RHS \: }$

We know,

$\sf:\longmapsto{ \cot \theta = \frac{ \cos \theta}{ \sin \theta } }$

Then,

$\sf:\longmapsto{ \cancel{ \sin \theta} \: \frac{ \cos \theta }{ \cancel{ \sin \theta}} = \cos \theta } \\ \\ \sf:\longmapsto{ \cos \theta = \cos \theta} \: \: \: \: \: \: \: \: \: \:$

Hence Proved !

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